NagaiHondaForce.cpp

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#include "NagaiHondaForce.hpp"

template<unsigned DIM>
NagaiHondaForce<DIM>::NagaiHondaForce()
   : AbstractForce<DIM>(),
     mNagaiHondaDeformationEnergyParameter(100.0), // This is 1.0 in the Nagai & Honda paper
     mNagaiHondaMembraneSurfaceEnergyParameter(10.0), // This is 0.1 the Nagai & Honda paper
     mNagaiHondaCellCellAdhesionEnergyParameter(1.0), // This is 0.01 the Nagai & Honda paper
     mNagaiHondaCellBoundaryAdhesionEnergyParameter(1.0), // This is 0.01 the Nagai & Honda paper
     mMatureCellTargetArea(1.0)
{
}

template<unsigned DIM>
NagaiHondaForce<DIM>::~NagaiHondaForce()
{
}

template<unsigned DIM>
void NagaiHondaForce<DIM>::AddForceContribution(std::vector<c_vector<double, DIM> >& rForces,
                                                AbstractCellPopulation<DIM>& rCellPopulation)
{
    // Throw an exception message if not using a VertexBasedCellPopulation
    if (dynamic_cast<VertexBasedCellPopulation<DIM>*>(&rCellPopulation) == NULL)
    {
        EXCEPTION("NagaiHondaForce is to be used with a VertexBasedCellPopulation only");
    }

    // Helper variable that is a static cast of the cell population
    VertexBasedCellPopulation<DIM>* p_cell_population = static_cast<VertexBasedCellPopulation<DIM>*>(&rCellPopulation);

    // Iterate over vertices in the cell population
    for (unsigned node_index=0; node_index<p_cell_population->GetNumNodes(); node_index++)
    {
        // Compute the force on this node

        /*
         * The force on this Node is given by the gradient of the total free
         * energy of the CellPopulation, evaluated at the position of the vertex. This
         * free energy is the sum of the free energies of all CellPtrs in
         * the cell population. The free energy of each CellPtr is comprised of three
         * parts - a cell deformation energy, a membrane surface tension energy
         * and an adhesion energy.
         *
         * Note that since the movement of this Node only affects the free energy
         * of the three CellPtrs containing it, we can just consider the
         * contributions to the free energy gradient from each of these three
         * CellPtrs.
         */

        c_vector<double, DIM> deformation_contribution = zero_vector<double>(DIM);
        c_vector<double, DIM> membrane_surface_tension_contribution = zero_vector<double>(DIM);
        c_vector<double, DIM> adhesion_contribution = zero_vector<double>(DIM);

        // Find the indices of the elements owned by this node
        std::set<unsigned> containing_elem_indices = p_cell_population->GetNode(node_index)->rGetContainingElementIndices();

        // Iterate over these elements
        for (std::set<unsigned>::iterator iter = containing_elem_indices.begin();
             iter != containing_elem_indices.end();
             ++iter)
        {
            // Get this element and its index
            VertexElement<DIM, DIM>* p_element = p_cell_population->GetElement(*iter);
            unsigned element_index = p_element->GetIndex();

            // Find the local index of this node in this element
            unsigned local_index = p_element->GetNodeLocalIndex(node_index);

            /******** Start of deformation force calculation ********/

            // Compute the area of this element and its gradient at this node
            double element_area = p_cell_population->rGetMesh().GetVolumeOfElement(*iter);
            c_vector<double, DIM> element_area_gradient = p_cell_population->rGetMesh().GetAreaGradientOfElementAtNode(p_element, local_index);

            // Get the target area of the cell
            double cell_target_area = GetTargetAreaOfCell(p_cell_population->GetCellUsingLocationIndex(element_index));

            // Add the force contribution from this cell's deformation energy (note the minus sign)
            deformation_contribution -= 2*GetNagaiHondaDeformationEnergyParameter()*(element_area - cell_target_area)*element_area_gradient;

            /******** End of deformation force calculation *************/

            /******** Start of membrane force calculation ***********/

            // Compute the perimeter of the element and its gradient at this node
            double element_perimeter = p_cell_population->rGetMesh().GetSurfaceAreaOfElement(*iter);
            c_vector<double, DIM> element_perimeter_gradient = p_cell_population->rGetMesh().GetPerimeterGradientOfElementAtNode(p_element, local_index);

            // Get the target perimeter of the cell
            double cell_target_perimeter = 2*sqrt(M_PI*cell_target_area);

            // Add the force contribution from this cell's membrane surface tension (note the minus sign)
            membrane_surface_tension_contribution -= 2*GetNagaiHondaMembraneSurfaceEnergyParameter()*(element_perimeter - cell_target_perimeter)*element_perimeter_gradient;

            /******** End of membrane force calculation **********/

            /******** Start of adhesion force calculation ***********/

            // Get the current, previous and next nodes in this element
            Node<DIM>* p_current_node = p_element->GetNode(local_index);

            unsigned previous_node_local_index = (p_element->GetNumNodes()+local_index-1)%(p_element->GetNumNodes());
            Node<DIM>* p_previous_node = p_element->GetNode(previous_node_local_index);

            unsigned next_node_local_index = (local_index+1)%(p_element->GetNumNodes());
            Node<DIM>* p_next_node = p_element->GetNode(next_node_local_index);

            // Compute the adhesion parameter for each of these edges
            double previous_edge_adhesion_parameter;
            double next_edge_adhesion_parameter;

            previous_edge_adhesion_parameter = GetAdhesionParameter(p_previous_node, p_current_node, *p_cell_population);
            next_edge_adhesion_parameter = GetAdhesionParameter(p_current_node, p_next_node, *p_cell_population);

            // Compute the gradient of the edge of the cell ending in this node
            c_vector<double, DIM> previous_edge_gradient = p_cell_population->rGetMesh().GetPreviousEdgeGradientOfElementAtNode(p_element, local_index);

            // Compute the gradient of the edge of the cell starting in this node
            c_vector<double, DIM> next_edge_gradient = p_cell_population->rGetMesh().GetNextEdgeGradientOfElementAtNode(p_element, local_index);

            // Add the force contribution from cell-cell and cell-boundary adhesion (note the minus sign)
            adhesion_contribution -= previous_edge_adhesion_parameter*previous_edge_gradient + next_edge_adhesion_parameter*next_edge_gradient;

            /******** End of adhesion force calculation *************/
        }

        c_vector<double, DIM> force_on_node = deformation_contribution +
                                              membrane_surface_tension_contribution +
                                              adhesion_contribution;

        rForces[node_index] += force_on_node;
    }
}

template<unsigned DIM>
double NagaiHondaForce<DIM>::GetAdhesionParameter(Node<DIM>* pNodeA, Node<DIM>* pNodeB, VertexBasedCellPopulation<DIM>& rVertexCellPopulation)
{
    // Find the indices of the elements owned by each node
    std::set<unsigned> elements_containing_nodeA = pNodeA->rGetContainingElementIndices();
    std::set<unsigned> elements_containing_nodeB = pNodeB->rGetContainingElementIndices();

    // Find common elements
    std::set<unsigned> shared_elements;
    std::set_intersection(elements_containing_nodeA.begin(),
                          elements_containing_nodeA.end(),
                          elements_containing_nodeB.begin(),
                          elements_containing_nodeB.end(),
                          std::inserter(shared_elements, shared_elements.begin()));

    // Check that the nodes have a common edge
    assert(!shared_elements.empty());

    double adhesion_parameter = GetNagaiHondaCellCellAdhesionEnergyParameter();

    // If the edge corresponds to a single element, then the cell is on the boundary
    if (shared_elements.size() == 1)
    {
        adhesion_parameter = GetNagaiHondaCellBoundaryAdhesionEnergyParameter();
    }

    return adhesion_parameter;
}

template<unsigned DIM>
double NagaiHondaForce<DIM>::GetNagaiHondaDeformationEnergyParameter()
{
    return mNagaiHondaDeformationEnergyParameter;
}

template<unsigned DIM>
double NagaiHondaForce<DIM>::GetNagaiHondaMembraneSurfaceEnergyParameter()
{
    return mNagaiHondaMembraneSurfaceEnergyParameter;
}

template<unsigned DIM>
double NagaiHondaForce<DIM>::GetNagaiHondaCellCellAdhesionEnergyParameter()
{
    return mNagaiHondaCellCellAdhesionEnergyParameter;
}

template<unsigned DIM>
double NagaiHondaForce<DIM>::GetNagaiHondaCellBoundaryAdhesionEnergyParameter()
{
    return mNagaiHondaCellBoundaryAdhesionEnergyParameter;
}

template<unsigned DIM>
void NagaiHondaForce<DIM>::SetNagaiHondaDeformationEnergyParameter(double deformationEnergyParameter)
{
    mNagaiHondaDeformationEnergyParameter = deformationEnergyParameter;
}

template<unsigned DIM>
void NagaiHondaForce<DIM>::SetNagaiHondaMembraneSurfaceEnergyParameter(double membraneSurfaceEnergyParameter)
{
    mNagaiHondaMembraneSurfaceEnergyParameter = membraneSurfaceEnergyParameter;
}

template<unsigned DIM>
void NagaiHondaForce<DIM>::SetNagaiHondaCellCellAdhesionEnergyParameter(double cellCellAdhesionEnergyParameter)
{
    mNagaiHondaCellCellAdhesionEnergyParameter = cellCellAdhesionEnergyParameter;
}

template<unsigned DIM>
void NagaiHondaForce<DIM>::SetNagaiHondaCellBoundaryAdhesionEnergyParameter(double cellBoundaryAdhesionEnergyParameter)
{
    mNagaiHondaCellBoundaryAdhesionEnergyParameter = cellBoundaryAdhesionEnergyParameter;
}

template<unsigned DIM>
double NagaiHondaForce<DIM>::GetTargetAreaOfCell(const CellPtr pCell) const
{
    // Get target area A of a healthy cell in S, G2 or M phase
    double cell_target_area = mMatureCellTargetArea;

    double cell_age = pCell->GetAge();
    double g1_duration = pCell->GetCellCycleModel()->GetG1Duration();

    // If the cell is differentiated then its G1 duration is infinite
    if (g1_duration == DBL_MAX) // don't use magic number, compare to DBL_MAX
    {
        // This is just for fixed cell-cycle models, need to work out how to find the g1 duration
        g1_duration = pCell->GetCellCycleModel()->GetTransitCellG1Duration();
    }

    if (pCell->HasCellProperty<ApoptoticCellProperty>())
    {
        // Age of cell when apoptosis begins
        if (pCell->GetStartOfApoptosisTime() - pCell->GetBirthTime() < g1_duration)
        {
            cell_target_area *= 0.5*(1 + (pCell->GetStartOfApoptosisTime() - pCell->GetBirthTime())/g1_duration);
        }

        // The target area of an apoptotic cell decreases linearly to zero (and past it negative)
        cell_target_area = cell_target_area - 0.5*cell_target_area/(pCell->GetApoptosisTime())*(SimulationTime::Instance()->GetTime()-pCell->GetStartOfApoptosisTime());

        // Don't allow a negative target area
        if (cell_target_area < 0)
        {
            cell_target_area = 0;
        }
    }
    else
    {
        // The target area of a proliferating cell increases linearly from A/2 to A over the course of the G1 phase
        if (cell_age < g1_duration)
        {
            cell_target_area *= 0.5*(1 + cell_age/g1_duration);
        }
    }

    return cell_target_area;
}

template<unsigned DIM>
double NagaiHondaForce<DIM>::GetMatureCellTargetArea() const
{
    return mMatureCellTargetArea;
}

template<unsigned DIM>
void NagaiHondaForce<DIM>::SetMatureCellTargetArea(double matureCellTargetArea)
{
    assert(matureCellTargetArea >= 0.0);
    mMatureCellTargetArea = matureCellTargetArea;
}

template<unsigned DIM>
void NagaiHondaForce<DIM>::OutputForceParameters(out_stream& rParamsFile)
{
    *rParamsFile << "\t\t\t<NagaiHondaDeformationEnergyParameter>" << mNagaiHondaDeformationEnergyParameter << "</NagaiHondaDeformationEnergyParameter>\n";
    *rParamsFile << "\t\t\t<NagaiHondaMembraneSurfaceEnergyParameter>" << mNagaiHondaMembraneSurfaceEnergyParameter << "</NagaiHondaMembraneSurfaceEnergyParameter>\n";
    *rParamsFile << "\t\t\t<NagaiHondaCellCellAdhesionEnergyParameter>" << mNagaiHondaCellCellAdhesionEnergyParameter << "</NagaiHondaCellCellAdhesionEnergyParameter>\n";
    *rParamsFile << "\t\t\t<NagaiHondaCellBoundaryAdhesionEnergyParameter>" << mNagaiHondaCellBoundaryAdhesionEnergyParameter << "</NagaiHondaCellBoundaryAdhesionEnergyParameter>\n";
    *rParamsFile << "\t\t\t<MatureCellTargetArea>" << mMatureCellTargetArea << "</MatureCellTargetArea>\n";

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

// Explicit instantiation

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

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