CaBasedCellPopulation.cpp

/*
 
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*/
 
#include <boost/scoped_array.hpp>
 
#include "CaBasedCellPopulation.hpp"
#include "MutableMesh.hpp"
#include "AbstractCaUpdateRule.hpp"
#include "AbstractCaSwitchingUpdateRule.hpp"
#include "RandomNumberGenerator.hpp"
#include "CellLocationIndexWriter.hpp"
#include "ExclusionCaBasedDivisionRule.hpp"
#include "NodesOnlyMesh.hpp"
#include "ApoptoticCellProperty.hpp"
 
// Needed to convert mesh in order to write nodes to VTK (visualize as glyphs)
#include "VtkMeshWriter.hpp"
 
// LCOV_EXCL_START
template<unsigned DIM>
void CaBasedCellPopulation<DIM>::Validate()
{
    NEVER_REACHED;
}
// LCOV_EXCL_STOP
 
template<unsigned DIM>
CaBasedCellPopulation<DIM>::CaBasedCellPopulation(PottsMesh<DIM>& rMesh,
                                                        std::vector<CellPtr>& rCells,
                                                        const std::vector<unsigned> locationIndices,
                                                        unsigned latticeCarryingCapacity,
                                                        bool deleteMesh,
                                                        bool validate)
    : AbstractOnLatticeCellPopulation<DIM>(rMesh, rCells, locationIndices, deleteMesh),
      mLatticeCarryingCapacity(latticeCarryingCapacity)
{
    mAvailableSpaces = std::vector<unsigned>(this->GetNumNodes(), latticeCarryingCapacity);
    mpCaBasedDivisionRule.reset(new ExclusionCaBasedDivisionRule<DIM>());
 
    // This must always be true
    assert(this->mCells.size() <= this->mrMesh.GetNumNodes()*latticeCarryingCapacity);
 
    if (locationIndices.empty())
    {
        EXCEPTION("No location indices being passed. Specify where cells lie before creating the cell population.");
    }
    else
    {
        // Create a set of node indices corresponding to empty sites.
        // Note iterating over mCells is OK as it has the same order as location indices at this point (its just coppied from rCells)
        std::list<CellPtr>::iterator it = this->mCells.begin();
        for (unsigned i=0; it != this->mCells.end(); ++it, ++i)
        {
            assert(i < locationIndices.size());
            if (!IsSiteAvailable(locationIndices[i],*it))
            {
                EXCEPTION("One of the lattice sites has more cells than the carrying capacity. Check the initial cell locations.");
            }
            mAvailableSpaces[locationIndices[i]]--;
        }
    }
    if (validate)
    {
        EXCEPTION("There is no validation for CaBasedCellPopulation.");
    }
}
 
template<unsigned DIM>
CaBasedCellPopulation<DIM>::CaBasedCellPopulation(PottsMesh<DIM>& rMesh)
    : AbstractOnLatticeCellPopulation<DIM>(rMesh)
{
}
 
template<unsigned DIM>
CaBasedCellPopulation<DIM>::~CaBasedCellPopulation()
{
    if (this->mDeleteMesh)
    {
        delete &this->mrMesh;
    }
}
 
template<unsigned DIM>
std::vector<unsigned>& CaBasedCellPopulation<DIM>::rGetAvailableSpaces()
{
    return mAvailableSpaces;
}
 
template<unsigned DIM>
bool CaBasedCellPopulation<DIM>::IsSiteAvailable(unsigned index, CellPtr pCell)
{
    return (mAvailableSpaces[index] != 0);
}
 
template<unsigned DIM>
PottsMesh<DIM>& CaBasedCellPopulation<DIM>::rGetMesh()
{
    return static_cast<PottsMesh<DIM>& >((this->mrMesh));
}
 
template<unsigned DIM>
const PottsMesh<DIM>& CaBasedCellPopulation<DIM>::rGetMesh() const
{
    return static_cast<PottsMesh<DIM>& >((this->mrMesh));
}
 
template<unsigned DIM>
TetrahedralMesh<DIM, DIM>* CaBasedCellPopulation<DIM>::GetTetrahedralMeshForPdeModifier()
{
    std::vector<Node<DIM>*> temp_nodes;
 
    // Create nodes at the centre of the cells
    unsigned cell_index = 0;
    for (typename AbstractCellPopulation<DIM>::Iterator cell_iter = this->Begin();
         cell_iter != this->End();
         ++cell_iter)
    {
        temp_nodes.push_back(new Node<DIM>(cell_index, this->GetLocationOfCellCentre(*cell_iter)));
        cell_index++;
    }
 
    return new MutableMesh<DIM,DIM>(temp_nodes);
}
 
template<unsigned DIM>
Node<DIM>* CaBasedCellPopulation<DIM>::GetNode(unsigned index)
{
    return this->mrMesh.GetNode(index);
}
 
template<unsigned DIM>
unsigned CaBasedCellPopulation<DIM>::GetNumNodes()
{
    return this->mrMesh.GetNumNodes();
}
 
template<unsigned DIM>
std::set<unsigned> CaBasedCellPopulation<DIM>::GetNeighbouringLocationIndices(CellPtr pCell)
{
    unsigned index = this->GetLocationIndexUsingCell(pCell);
    std::set<unsigned> candidates = static_cast<PottsMesh<DIM>& >((this->mrMesh)).GetMooreNeighbouringNodeIndices(index);
 
    std::set<unsigned> neighbour_indices;
    for (std::set<unsigned>::iterator iter = candidates.begin();
         iter != candidates.end();
         ++iter)
    {
        if (!IsSiteAvailable(*iter, pCell))
        {
            neighbour_indices.insert(*iter);
        }
    }
 
    return neighbour_indices;
}
 
template<unsigned DIM>
c_vector<double, DIM> CaBasedCellPopulation<DIM>::GetLocationOfCellCentre(CellPtr pCell)
{
    return this->mrMesh.GetNode(this->GetLocationIndexUsingCell(pCell))->rGetLocation();
}
 
template<unsigned DIM>
Node<DIM>* CaBasedCellPopulation<DIM>::GetNodeCorrespondingToCell(CellPtr pCell)
{
    return this->mrMesh.GetNode(this->GetLocationIndexUsingCell(pCell));
}
 
template<unsigned DIM>
void CaBasedCellPopulation<DIM>::AddCellUsingLocationIndex(unsigned index, CellPtr pCell)
{
    if (!IsSiteAvailable(index, pCell))
    {
        EXCEPTION("No available spaces at location index " << index << ".");
    }
 
    mAvailableSpaces[index]--;
    AbstractCellPopulation<DIM,DIM>::AddCellUsingLocationIndex(index, pCell);
}
 
template<unsigned DIM>
void CaBasedCellPopulation<DIM>::RemoveCellUsingLocationIndex(unsigned index, CellPtr pCell)
{
    AbstractCellPopulation<DIM,DIM>::RemoveCellUsingLocationIndex(index, pCell);
 
    mAvailableSpaces[index]++;
 
    assert(mAvailableSpaces[index] <= mLatticeCarryingCapacity);
}
 
template<unsigned DIM>
bool CaBasedCellPopulation<DIM>::IsRoomToDivide(CellPtr pCell)
{
    return mpCaBasedDivisionRule->IsRoomToDivide(pCell, *this);
}
 
template<unsigned DIM>
CellPtr CaBasedCellPopulation<DIM>::AddCell(CellPtr pNewCell, CellPtr pParentCell)
{
    unsigned daughter_node_index = mpCaBasedDivisionRule->CalculateDaughterNodeIndex(pNewCell,pParentCell,*this);
 
    // Associate the new cell with the neighbouring node
    this->mCells.push_back(pNewCell);
 
    // Update location cell map
    CellPtr p_created_cell = this->mCells.back();
    AddCellUsingLocationIndex(daughter_node_index,p_created_cell);
 
    return p_created_cell;
}
 
template<unsigned DIM>
double CaBasedCellPopulation<DIM>:: EvaluateDivisionPropensity(unsigned currentNodeIndex,
                                                               unsigned targetNodeIndex,
                                                               CellPtr pCell)
{
    return 1.0;
}
 
template<unsigned DIM>
unsigned CaBasedCellPopulation<DIM>::RemoveDeadCells()
{
    unsigned num_removed = 0;
 
    for (std::list<CellPtr>::iterator cell_iter = this->mCells.begin();
         cell_iter != this->mCells.end();
         )
    {
        if ((*cell_iter)->IsDead())
        {
            // Get the location index corresponding to this cell
            unsigned location_index = this->GetLocationIndexUsingCell(*cell_iter);
 
            // Use this to remove the cell from the population
            RemoveCellUsingLocationIndex(location_index, (*cell_iter));
 
            // Erase cell and update counter
            cell_iter = this->mCells.erase(cell_iter);
            num_removed++;
        }
        else
        {
            ++cell_iter;
        }
    }
    return num_removed;
}
 
template<unsigned DIM>
void CaBasedCellPopulation<DIM>::UpdateCellLocations(double dt)
{
    /*
     * Here we loop over the nodes and calculate the probability of moving
     * and then select the node to move to.
     */
    if (!(this->mUpdateRuleCollection.empty()))
    {
        // Iterate over cells
        for (std::list<CellPtr>::iterator cell_iter = this->mCells.begin();
             cell_iter != this->mCells.end();
             ++cell_iter)
        {
            // Loop over neighbours and calculate probability of moving (make sure all probabilities are <1)
            unsigned node_index = this->GetLocationIndexUsingCell(*cell_iter);
 
            // Find a random available neighbouring node to overwrite current site
            std::set<unsigned> neighbouring_node_indices = static_cast<PottsMesh<DIM>& >((this->mrMesh)).GetMooreNeighbouringNodeIndices(node_index);
            std::vector<double> neighbouring_node_propensities;
            std::vector<unsigned> neighbouring_node_indices_vector;
 
            if (!neighbouring_node_indices.empty())
            {
                unsigned num_neighbours = neighbouring_node_indices.size();
                double probability_of_not_moving = 1.0;
 
                for (std::set<unsigned>::iterator iter = neighbouring_node_indices.begin();
                     iter != neighbouring_node_indices.end();
                     ++iter)
                {
                    double probability_of_moving = 0.0;
 
                    neighbouring_node_indices_vector.push_back(*iter);
 
                    if (IsSiteAvailable(*iter, *cell_iter))
                    {
                        // Iterating over the update rule
                        for (typename std::vector<boost::shared_ptr<AbstractUpdateRule<DIM> > >::iterator iter_rule = this->mUpdateRuleCollection.begin();
                             iter_rule != this->mUpdateRuleCollection.end();
                             ++iter_rule)
                        {
                            // This static cast is fine, since we assert the update rule must be a CA update rule in AddUpdateRule()
                            double p = (boost::static_pointer_cast<AbstractCaUpdateRule<DIM> >(*iter_rule))->EvaluateProbability(node_index, *iter, *this, dt, 1, *cell_iter);
                            probability_of_moving += p;
                            if (probability_of_moving < 0)
                            {
                                EXCEPTION("The probability of cellular movement is smaller than zero. In order to prevent it from happening you should change your time step and parameters");
                            }
 
                            if (probability_of_moving > 1)
                            {
                                EXCEPTION("The probability of the cellular movement is bigger than one. In order to prevent it from happening you should change your time step and parameters");
                            }
                        }
 
                        probability_of_not_moving -= probability_of_moving;
                        neighbouring_node_propensities.push_back(probability_of_moving);
                    }
                    else
                    {
                        neighbouring_node_propensities.push_back(0.0);
                    }
                }
                if (probability_of_not_moving < 0)
                {
                    EXCEPTION("The probability of the cell not moving is smaller than zero. In order to prevent it from happening you should change your time step and parameters");
                }
 
                // Sample random number to specify which move to make
                RandomNumberGenerator* p_gen = RandomNumberGenerator::Instance();
                double random_number = p_gen->ranf();
 
                double total_probability = 0.0;
                for (unsigned counter=0; counter<num_neighbours; counter++)
                {
                    total_probability += neighbouring_node_propensities[counter];
                    if (total_probability >= random_number)
                    {
                        // Move the cell to this neighbour location
                        unsigned chosen_neighbour_location_index = neighbouring_node_indices_vector[counter];
                        this->MoveCellInLocationMap((*cell_iter), node_index, chosen_neighbour_location_index);
                        break;
                    }
                }
                // If loop completes with total_probability < random_number then stay in the same location
            }
            else
            {
                // Each node in the mesh must have at least one neighbour
                NEVER_REACHED;
            }
        }
    }
 
    /*
     * Here we loop over the nodes and select a neighbour to test if
     * the cells (associated with the nodes) should swap locations
     * or if a cell should move to an empty node
     * Note this currently only works for latticeCarryingCapacity = 1
     */
    if (!(mSwitchingUpdateRuleCollection.empty()))
    {
        assert(mLatticeCarryingCapacity == 1);
 
        RandomNumberGenerator* p_gen = RandomNumberGenerator::Instance();
        unsigned num_nodes = this->mrMesh.GetNumNodes();
 
        // Randomly permute mUpdateRuleCollection if specified
        if (this->mIterateRandomlyOverUpdateRuleCollection)
        {
            // Randomly permute mUpdateRuleCollection
            p_gen->Shuffle(mSwitchingUpdateRuleCollection);
        }
 
        for (unsigned i=0; i<num_nodes; i++)
        {
            unsigned node_index;
 
            if (this->mUpdateNodesInRandomOrder)
            {
                node_index = p_gen->randMod(num_nodes);
            }
            else
            {
                // Loop over nodes in index order
                node_index = i%num_nodes;
            }
 
            // Find a random available neighbouring node to switch cells with the current site
            std::set<unsigned> neighbouring_node_indices = static_cast<PottsMesh<DIM>& >((this->mrMesh)).GetMooreNeighbouringNodeIndices(node_index);
 
            unsigned neighbour_location_index;
 
            if (!neighbouring_node_indices.empty())
            {
                unsigned num_neighbours = neighbouring_node_indices.size();
                unsigned chosen_neighbour = p_gen->randMod(num_neighbours);
 
                std::set<unsigned>::iterator neighbour_iter = neighbouring_node_indices.begin();
                for (unsigned j=0; j<chosen_neighbour; j++)
                {
                    neighbour_iter++;
                }
                neighbour_location_index = *neighbour_iter;
 
                bool is_cell_on_node_index = mAvailableSpaces[node_index] == 0 ? true : false;
                bool is_cell_on_neighbour_location_index = mAvailableSpaces[neighbour_location_index] == 0 ? true : false;
 
                if (is_cell_on_node_index || is_cell_on_neighbour_location_index)
                {
                    double probability_of_switch = 0.0;
 
                    // Now add contributions to the probability from each CA switching update rule
                    for (typename std::vector<boost::shared_ptr<AbstractUpdateRule<DIM> > >::iterator iter_rule = mSwitchingUpdateRuleCollection.begin();
                         iter_rule != mSwitchingUpdateRuleCollection.end();
                         ++iter_rule)
                    {
                        // This static cast is fine, since we assert the update rule must be a CA switching update rule in AddUpdateRule()
                        double p = (boost::static_pointer_cast<AbstractCaSwitchingUpdateRule<DIM> >(*iter_rule))->EvaluateSwitchingProbability(node_index, neighbour_location_index, *this, dt, 1);
                        probability_of_switch += p;
                    }
 
                    assert(probability_of_switch >= 0);
                    assert(probability_of_switch <= 1);
 
                    // Generate a uniform random number to do the random switch
                    double random_number = p_gen->ranf();
 
                    if (random_number < probability_of_switch)
                    {
                        if (is_cell_on_node_index && is_cell_on_neighbour_location_index)
                        {
                            // Swap the cells associated with the node and the neighbour node
                            CellPtr p_cell = this->GetCellUsingLocationIndex(node_index);
                            CellPtr p_neighbour_cell = this->GetCellUsingLocationIndex(neighbour_location_index);
 
                            // Remove the cells from their current location
                            RemoveCellUsingLocationIndex(node_index, p_cell);
                            RemoveCellUsingLocationIndex(neighbour_location_index, p_neighbour_cell);
 
                            // Add cells to their new locations
                            AddCellUsingLocationIndex(node_index, p_neighbour_cell);
                            AddCellUsingLocationIndex(neighbour_location_index, p_cell);
                        }
                        else if (is_cell_on_node_index && !is_cell_on_neighbour_location_index)
                        {
                            // Move the cells associated with the node to the neighbour node
                            CellPtr p_cell = this->GetCellUsingLocationIndex(node_index);
                            RemoveCellUsingLocationIndex(node_index, p_cell);
                            AddCellUsingLocationIndex(neighbour_location_index, p_cell);
                        }
                        else if (!is_cell_on_node_index && is_cell_on_neighbour_location_index)
                        {
                            // Move the cell associated with the neighbour node onto the node
                            CellPtr p_neighbour_cell = this->GetCellUsingLocationIndex(neighbour_location_index);
                            RemoveCellUsingLocationIndex(neighbour_location_index, p_neighbour_cell);
                            AddCellUsingLocationIndex(node_index, p_neighbour_cell);
                        }
                        else
                        {
                            NEVER_REACHED;
                        }
                    }
                }
            }
        }
    }
}
 
template<unsigned DIM>
bool CaBasedCellPopulation<DIM>::IsCellAssociatedWithADeletedLocation(CellPtr pCell)
{
    return false;
}
 
template<unsigned DIM>
void CaBasedCellPopulation<DIM>::Update(bool hasHadBirthsOrDeaths)
{
}
 
template<unsigned DIM>
void CaBasedCellPopulation<DIM>::AcceptPopulationWriter(boost::shared_ptr<AbstractCellPopulationWriter<DIM, DIM> > pPopulationWriter)
{
    pPopulationWriter->Visit(this);
}
 
template<unsigned DIM>
void CaBasedCellPopulation<DIM>::AcceptPopulationCountWriter(boost::shared_ptr<AbstractCellPopulationCountWriter<DIM, DIM> > pPopulationCountWriter)
{
    pPopulationCountWriter->Visit(this);
}
 
template<unsigned DIM>
void CaBasedCellPopulation<DIM>::AcceptPopulationEventWriter(boost::shared_ptr<AbstractCellPopulationEventWriter<DIM, DIM> > pPopulationEventWriter)
{
    pPopulationEventWriter->Visit(this);
}
 
template<unsigned DIM>
void CaBasedCellPopulation<DIM>::AcceptCellWriter(boost::shared_ptr<AbstractCellWriter<DIM, DIM> > pCellWriter, CellPtr pCell)
{
    pCellWriter->VisitCell(pCell, this);
}
 
template<unsigned DIM>
void CaBasedCellPopulation<DIM>::OpenWritersFiles(OutputFileHandler& rOutputFileHandler)
{
    if (this->mOutputResultsForChasteVisualizer)
    {
        if (!this-> template HasWriter<CellLocationIndexWriter>())
        {
            this-> template AddCellWriter<CellLocationIndexWriter>();
        }
    }
 
    AbstractCellPopulation<DIM>::OpenWritersFiles(rOutputFileHandler);
}
 
template<unsigned DIM>
double CaBasedCellPopulation<DIM>::GetVolumeOfCell(CellPtr pCell)
{
    double cell_volume = 1.0;
    return cell_volume;
}
 
template<unsigned DIM>
double CaBasedCellPopulation<DIM>::GetWidth(const unsigned& rDimension)
{
    double width = this->mrMesh.GetWidth(rDimension);
    return width;
}
 
template<unsigned DIM>
void CaBasedCellPopulation<DIM>::AddUpdateRule(boost::shared_ptr<AbstractUpdateRule<DIM> > pUpdateRule)
{
    // The update rule must be derived from AbstractCaUpdateRule or AbstractCaSwitchingUpdateRule
    assert(bool(dynamic_cast<AbstractCaUpdateRule<DIM>*>(pUpdateRule.get())) ||
           bool(dynamic_cast<AbstractCaSwitchingUpdateRule<DIM>*>(pUpdateRule.get())));
 
    if (bool(dynamic_cast<AbstractCaUpdateRule<DIM>*>(pUpdateRule.get())))
    {
        this->mUpdateRuleCollection.push_back(pUpdateRule);
    }
    else
    {
        mSwitchingUpdateRuleCollection.push_back(pUpdateRule);
    }
}
 
template<unsigned DIM>
void CaBasedCellPopulation<DIM>::RemoveAllUpdateRules()
{
    // Clear mSwitchingUpdateRuleCollection
    mSwitchingUpdateRuleCollection.clear();
 
    // Clear mUpdateRuleCollection
    AbstractOnLatticeCellPopulation<DIM>::RemoveAllUpdateRules();
}
 
template<unsigned DIM>
const std::vector<boost::shared_ptr<AbstractUpdateRule<DIM> > > CaBasedCellPopulation<DIM>::GetUpdateRuleCollection() const
{
    std::vector<boost::shared_ptr<AbstractUpdateRule<DIM> > > update_rules;
 
    for (unsigned i=0; i<this->mUpdateRuleCollection.size(); i++)
    {
        update_rules.push_back(this->mUpdateRuleCollection[i]);
    }
    for (unsigned i=0; i<mSwitchingUpdateRuleCollection.size(); i++)
    {
        update_rules.push_back(mSwitchingUpdateRuleCollection[i]);
    }
 
    return update_rules;
}
 
template<unsigned DIM>
boost::shared_ptr<AbstractCaBasedDivisionRule<DIM> > CaBasedCellPopulation<DIM>::GetCaBasedDivisionRule()
{
    return mpCaBasedDivisionRule;
}
 
template<unsigned DIM>
void CaBasedCellPopulation<DIM>::SetCaBasedDivisionRule(boost::shared_ptr<AbstractCaBasedDivisionRule<DIM> > pCaBasedDivisionRule)
{
    mpCaBasedDivisionRule = pCaBasedDivisionRule;
}
 
template<unsigned DIM>
void CaBasedCellPopulation<DIM>::OutputCellPopulationParameters(out_stream& rParamsFile)
{
    // Add the division rule parameters
    *rParamsFile << "\t\t<CaBasedDivisionRule>\n";
    mpCaBasedDivisionRule->OutputCellCaBasedDivisionRuleInfo(rParamsFile);
    *rParamsFile << "\t\t</CaBasedDivisionRule>\n";
 
    // Call method on direct parent class
    AbstractOnLatticeCellPopulation<DIM>::OutputCellPopulationParameters(rParamsFile);
}
 
template<unsigned DIM>
void CaBasedCellPopulation<DIM>::WriteVtkResultsToFile(const std::string& rDirectory)
{
#ifdef CHASTE_VTK
    // Store the present time as a string
    unsigned num_timesteps = SimulationTime::Instance()->GetTimeStepsElapsed();
    std::stringstream time;
    time << num_timesteps;
 
    // Store the number of cells for which to output data to VTK
    unsigned num_cells = this->GetNumRealCells();
 
    // When outputting any CellData, we assume that the first cell is representative of all cells
    unsigned num_cell_data_items = 0u;
    std::vector<std::string> cell_data_names;
    if (num_cells > 0u)
    {
        num_cell_data_items = this->Begin()->GetCellData()->GetNumItems();
        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);
    }
 
    // Create mesh writer for VTK output
    VtkMeshWriter<DIM, DIM> mesh_writer(rDirectory, "results_"+time.str(), false);
 
    // Create a counter to keep track of how many cells are at a lattice site
    unsigned num_sites = this->mrMesh.GetNumNodes();
    boost::scoped_array<unsigned> number_of_cells_at_site(new unsigned[num_sites]);
    for (unsigned i=0; i<num_sites; i++)
    {
        number_of_cells_at_site[i] = 0;
    }
 
    // Populate a vector of nodes associated with cell locations, by iterating through the list of cells
    std::vector<Node<DIM>*> nodes;
    unsigned node_index = 0;
    for (typename AbstractCellPopulation<DIM,DIM>::Iterator cell_iter = this->Begin();
         cell_iter != this->End();
         ++cell_iter)
    {
        // Get the location index of this cell and update the counter number_of_cells_at_site
        unsigned location_index = this->GetLocationIndexUsingCell(*cell_iter);
        number_of_cells_at_site[location_index]++;
        assert(number_of_cells_at_site[location_index] <= mLatticeCarryingCapacity);
 
        // Note that we define this vector before setting it as otherwise the profiling build will break (see #2367)
        c_vector<double, DIM> coords;
        coords = this->mrMesh.GetNode(location_index)->rGetLocation();
 
        // Move the coordinates slightly so that we can visualise all cells in a lattice site if there is more than one per site
        if (mLatticeCarryingCapacity > 1)
        {
            c_vector<double, DIM> offset;
 
            if (DIM == 2)
            {
                double angle = (double)number_of_cells_at_site[location_index]*2.0*M_PI/(double)mLatticeCarryingCapacity;
                offset[0] = 0.2*sin(angle);
                offset[1] = 0.2*cos(angle);
            }
            else
            {
                RandomNumberGenerator* p_gen = RandomNumberGenerator::Instance();
                for (unsigned i=0; i<DIM; i++)
                {
                    offset[i] = p_gen->ranf(); // This assumes that all sites are 1 unit apart
                }
            }
 
            for (unsigned i=0; i<DIM; i++)
            {
                coords[i] += offset[i];
            }
        }
 
        nodes.push_back(new Node<DIM>(node_index, coords, false));
        node_index++;
    }
 
    // Iterate over any cell writers that are present
    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
        // (using a default value of -1 to correspond to an empty lattice site)
        std::vector<double> vtk_cell_data(num_cells, -1.0);
 
        // Loop over cells
        unsigned cell_index = 0;
        for (typename AbstractCellPopulation<DIM,DIM>::Iterator cell_iter = this->Begin();
             cell_iter != this->End();
             ++cell_iter)
        {
            // Populate the vector of VTK cell data
            vtk_cell_data[cell_index] = (*cell_writer_iter)->GetCellDataForVtkOutput(*cell_iter, this);
            cell_index++;
        }
 
        mesh_writer.AddPointData((*cell_writer_iter)->GetVtkCellDataName(), vtk_cell_data);
    }
 
    // Loop over cells to output the cell data
    unsigned cell_index = 0;
    for (typename AbstractCellPopulation<DIM,DIM>::Iterator cell_iter = this->Begin();
         cell_iter != this->End();
         ++cell_iter)
    {
        for (unsigned var=0; var<num_cell_data_items; var++)
        {
            cell_data[var][cell_index] = cell_iter->GetCellData()->GetItem(cell_data_names[var]);
        }
        cell_index++;
    }
    for (unsigned var=0; var<num_cell_data_items; var++)
    {
        mesh_writer.AddPointData(cell_data_names[var], cell_data[var]);
    }
 
    /*
     * At present, the VTK writer can only write things which inherit from AbstractTetrahedralMeshWriter.
     * For now, we do an explicit conversion to NodesOnlyMesh. This can be written to VTK, then visualized
     * as glyphs in Paraview.
     */
    NodesOnlyMesh<DIM> temp_mesh;
 
    // Use an approximation of the node spacing as the interaction distance for the nodes only mesh. This is to
    // avoid rounding errors in distributed box collection.
    double volume = this->mrMesh.GetWidth(0);
    for (unsigned idx=1; idx<DIM; idx++)
    {
        volume *= this->mrMesh.GetWidth(idx);
    }
 
    double spacing;
    if (this->mrMesh.GetNumNodes() >0 && volume > 0.0)
    {
        spacing = std::pow(volume / double(this->mrMesh.GetNumNodes()), 1.0/double(DIM));
    }
    else
    {
        spacing = 1.0;
    }
 
    temp_mesh.ConstructNodesWithoutMesh(nodes, spacing * 1.2);
    mesh_writer.WriteFilesUsingMesh(temp_mesh);
 
    *(this->mpVtkMetaFile) << "        <DataSet timestep=\"";
    *(this->mpVtkMetaFile) << num_timesteps;
    *(this->mpVtkMetaFile) << "\" group=\"\" part=\"0\" file=\"results_";
    *(this->mpVtkMetaFile) << num_timesteps;
    *(this->mpVtkMetaFile) << ".vtu\"/>\n";
 
    // Tidy up
    for (unsigned i=0; i<nodes.size(); i++)
    {
        delete nodes[i];
    }
#endif //CHASTE_VTK
}
 
template<unsigned DIM>
double CaBasedCellPopulation<DIM>::GetCellDataItemAtPdeNode(
    unsigned pdeNodeIndex,
    std::string& rVariableName,
    bool dirichletBoundaryConditionApplies,
    double dirichletBoundaryValue)
{
    unsigned counter = 0;
    typename AbstractCellPopulation<DIM>::Iterator cell_iter = this->Begin();
    while (counter != pdeNodeIndex)
    {
        ++cell_iter;
        counter++;
    }
 
    double value = cell_iter->GetCellData()->GetItem(rVariableName);
 
    return value;
}
 
template<unsigned DIM>
bool CaBasedCellPopulation<DIM>::IsPdeNodeAssociatedWithNonApoptoticCell(unsigned pdeNodeIndex)
{
    // pdeNodeIndex corresponds to the 'position' of the cell to interrogate in the vector of cells
    typename AbstractCellPopulation<DIM>::Iterator cell_iter = this->Begin();
 
    assert(pdeNodeIndex < this->GetNumRealCells());
    for (unsigned i=0; i<pdeNodeIndex; i++)
    {
        ++cell_iter;
    }
    bool is_cell_apoptotic = cell_iter->template HasCellProperty<ApoptoticCellProperty>();
 
    return !is_cell_apoptotic;
}
 
// Explicit instantiation
template class CaBasedCellPopulation<1>;
template class CaBasedCellPopulation<2>;
template class CaBasedCellPopulation<3>;
 
// Serialization for Boost >= 1.36
#include "SerializationExportWrapperForCpp.hpp"
EXPORT_TEMPLATE_CLASS_SAME_DIMS(CaBasedCellPopulation)