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 in the Nagai & Honda paper.
     mNagaiHondaCellCellAdhesionEnergyParameter(0.5), // This corresponds to a value of 1.0 for
                                                      // the sigma parameter in the Nagai & Honda
                                                      // paper. In the paper, the sigma value is
                                                      // set to 0.01.
     mNagaiHondaCellBoundaryAdhesionEnergyParameter(1.0), // This is 0.01 in the Nagai & Honda paper
     mNagaiHondaTargetAreaParameter(1.0)
{
}
 
template<unsigned DIM>
NagaiHondaForce<DIM>::~NagaiHondaForce()
{
}
 
template<unsigned DIM>
void NagaiHondaForce<DIM>::AddForceContribution(AbstractCellPopulation<DIM>& rCellPopulation)
{
    // Throw an exception message if not using a VertexBasedCellPopulation
    if (dynamic_cast<VertexBasedCellPopulation<DIM>*>(&rCellPopulation) == nullptr)
    {
        EXCEPTION("NagaiHondaForce is to be used with a VertexBasedCellPopulation only");
    }
 
    // Define some helper variables
    VertexBasedCellPopulation<DIM>* p_cell_population = static_cast<VertexBasedCellPopulation<DIM>*>(&rCellPopulation);
    unsigned num_nodes = p_cell_population->GetNumNodes();
    unsigned num_elements = p_cell_population->GetNumElements();
 
    /*
     * Check if a subclass of AbstractTargetAreaModifier is being used by
     * interrogating the first cell (assuming either all cells, or no cells, in
     * the population have the CellData item "target area").
     */
    bool using_target_area_modifier = p_cell_population->Begin()->GetCellData()->HasItem("target area");
 
    // Begin by computing the area and perimeter of each element in the mesh, to avoid having to do this multiple times
    std::vector<double> element_areas(num_elements);
    std::vector<double> element_perimeters(num_elements);
    std::vector<double> target_areas(num_elements);
    for (typename VertexMesh<DIM,DIM>::VertexElementIterator elem_iter = p_cell_population->rGetMesh().GetElementIteratorBegin();
         elem_iter != p_cell_population->rGetMesh().GetElementIteratorEnd();
         ++elem_iter)
    {
        unsigned elem_index = elem_iter->GetIndex();
        element_areas[elem_index] = p_cell_population->rGetMesh().GetVolumeOfElement(elem_index);
        element_perimeters[elem_index] = p_cell_population->rGetMesh().GetSurfaceAreaOfElement(elem_index);
 
        if (using_target_area_modifier)
        {
            target_areas[elem_index] = p_cell_population->GetCellUsingLocationIndex(elem_index)->GetCellData()->GetItem("target area");
        }
        else
        {
            target_areas[elem_index] = mNagaiHondaTargetAreaParameter;
        }
    }
 
    // Iterate over vertices in the cell population
    for (unsigned node_index=0; node_index<num_nodes; node_index++)
    {
        Node<DIM>* p_this_node = p_cell_population->GetNode(node_index);
 
        /*
         * 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 CellPtrs containing it, we can just consider the contributions
         * to the free energy gradient from each of these 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, its index and its number of nodes
            VertexElement<DIM, DIM>* p_element = p_cell_population->GetElement(*iter);
            unsigned elem_index = p_element->GetIndex();
            unsigned num_nodes_elem = p_element->GetNumNodes();
 
            // Find the local index of this node in this element
            unsigned local_index = p_element->GetNodeLocalIndex(node_index);
 
            // Add the force contribution from this cell's deformation energy (note the minus sign)
            c_vector<double, DIM> element_area_gradient = p_cell_population->rGetMesh().GetAreaGradientOfElementAtNode(p_element, local_index);
            deformation_contribution -= 2*GetNagaiHondaDeformationEnergyParameter()*(element_areas[elem_index] - target_areas[elem_index])*element_area_gradient;
 
            // Get the previous and next nodes in this element
            unsigned previous_node_local_index = (num_nodes_elem+local_index-1)%num_nodes_elem;
            Node<DIM>* p_previous_node = p_element->GetNode(previous_node_local_index);
 
            unsigned next_node_local_index = (local_index+1)%num_nodes_elem;
            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 = GetAdhesionParameter(p_previous_node, p_this_node, *p_cell_population);
            double next_edge_adhesion_parameter = GetAdhesionParameter(p_this_node, p_next_node, *p_cell_population);
 
            // Compute the gradient of each these edges, computed at the present node
            c_vector<double, DIM> previous_edge_gradient = -p_cell_population->rGetMesh().GetNextEdgeGradientOfElementAtNode(p_element, previous_node_local_index);
            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;
 
            // Add the force contribution from this cell's membrane surface tension (note the minus sign)
            c_vector<double, DIM> element_perimeter_gradient;
            element_perimeter_gradient = previous_edge_gradient + next_edge_gradient;
            double cell_target_perimeter = 2*sqrt(M_PI*target_areas[elem_index]);
            membrane_surface_tension_contribution -= 2*GetNagaiHondaMembraneSurfaceEnergyParameter()*(element_perimeters[elem_index] - cell_target_perimeter)*element_perimeter_gradient;
        }
 
        c_vector<double, DIM> force_on_node = deformation_contribution + membrane_surface_tension_contribution + adhesion_contribution;
        p_cell_population->GetNode(node_index)->AddAppliedForceContribution(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>
double NagaiHondaForce<DIM>::GetNagaiHondaTargetAreaParameter()
{
    return mNagaiHondaTargetAreaParameter;
}
 
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>
void NagaiHondaForce<DIM>::SetNagaiHondaTargetAreaParameter(double nagaiHondaTargetAreaParameter)
{
    mNagaiHondaTargetAreaParameter = nagaiHondaTargetAreaParameter;
}
 
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<NagaiHondaTargetAreaParameter>" << mNagaiHondaTargetAreaParameter << "</NagaiHondaTargetAreaParameter>\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)