CryptProjectionForce.cpp

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*/
 
#include "CryptProjectionForce.hpp"
#include "MeshBasedCellPopulation.hpp"
#include "WntConcentration.hpp"
#include "StemCellProliferativeType.hpp"
 
#include <cmath>
 
CryptProjectionForce::CryptProjectionForce()
    : GeneralisedLinearSpringForce<2>(),
      mIncludeWntChemotaxis(false),
      mWntChemotaxisStrength(100.0)
{
    mA = WntConcentration<2>::Instance()->GetCryptProjectionParameterA();
    mB = WntConcentration<2>::Instance()->GetCryptProjectionParameterB();
}
 
CryptProjectionForce::~CryptProjectionForce()
{
}
 
void CryptProjectionForce::UpdateNode3dLocationMap(AbstractCellPopulation<2>& rCellPopulation)
{
    mNode3dLocationMap.clear();
 
    c_vector<double, 2> node_location_2d;
    c_vector<double, 3> node_location_3d;
 
    // Only consider nodes corresponding to real cells
    for (AbstractCellPopulation<2>::Iterator cell_iter = rCellPopulation.Begin();
         cell_iter != rCellPopulation.End();
         ++cell_iter)
    {
        // Get node index
        unsigned node_index = rCellPopulation.GetLocationIndexUsingCell(*cell_iter);
 
        // Get 3D location
        node_location_2d = rCellPopulation.GetLocationOfCellCentre(*cell_iter);
 
        node_location_3d[0] = node_location_2d[0];
        node_location_3d[1] = node_location_2d[1];
        node_location_3d[2] = CalculateCryptSurfaceHeightAtPoint(node_location_2d);
 
        // Add to map
        mNode3dLocationMap[node_index] = node_location_3d;
    }
}
 
double CryptProjectionForce::GetA() const
{
    return mA;
}
 
double CryptProjectionForce::GetB() const
{
    return mB;
}
 
void CryptProjectionForce::SetWntChemotaxisStrength(double wntChemotaxisStrength)
{
    assert(wntChemotaxisStrength >= 0.0);
    mWntChemotaxisStrength = wntChemotaxisStrength;
}
double CryptProjectionForce::GetWntChemotaxisStrength()
{
    return mWntChemotaxisStrength;
}
 
void CryptProjectionForce::SetWntChemotaxis(bool includeWntChemotaxis)
{
    mIncludeWntChemotaxis = includeWntChemotaxis;
}
 
double CryptProjectionForce::CalculateCryptSurfaceHeightAtPoint(const c_vector<double,2>& rNodeLocation)
{
    return mA*pow(norm_2(rNodeLocation), mB); // =z_coord;
}
 
double CryptProjectionForce::CalculateCryptSurfaceDerivativeAtPoint(const c_vector<double,2>& rNodeLocation)
{
    return mA*mB*pow(norm_2(rNodeLocation), (mB - 1.0));
}
 
c_vector<double,2> CryptProjectionForce::CalculateForceBetweenNodes(unsigned nodeAGlobalIndex, unsigned nodeBGlobalIndex, AbstractCellPopulation<2>& rCellPopulation)
{
    MeshBasedCellPopulation<2>* p_static_cast_cell_population = static_cast<MeshBasedCellPopulation<2>*>(&rCellPopulation);
 
    // We should only ever calculate the force between two distinct nodes
    assert(nodeAGlobalIndex != nodeBGlobalIndex);
 
    // Get the node locations in 2D
    c_vector<double,2> node_a_location_2d = rCellPopulation.GetNode(nodeAGlobalIndex)->rGetLocation();
    c_vector<double,2> node_b_location_2d = rCellPopulation.GetNode(nodeBGlobalIndex)->rGetLocation();
 
    // "Get the unit vector parallel to the line joining the two nodes" [GeneralisedLinearSpringForce]
 
    // Create a unit vector in the direction of the 3D spring
    c_vector<double,3> unit_difference = mNode3dLocationMap[nodeBGlobalIndex] - mNode3dLocationMap[nodeAGlobalIndex];
 
    // Calculate the distance between the two nodes
    double distance_between_nodes = norm_2(unit_difference);
    assert(distance_between_nodes > 0);
    assert(!std::isnan(distance_between_nodes));
 
    unit_difference /= distance_between_nodes;
 
    // If mUseCutOffLength has been set, then there is zero force between
    // two nodes located a distance apart greater than mUseCutOffLength
    if (this->mUseCutOffLength)
    {
        if (distance_between_nodes >= mMechanicsCutOffLength)
        {
            // Return zero (2D projected) force
            return zero_vector<double>(2);
        }
    }
 
    // Calculate the rest length of the spring connecting the two nodes
 
    double rest_length = 1.0;
 
    CellPtr p_cell_A = rCellPopulation.GetCellUsingLocationIndex(nodeAGlobalIndex);
    CellPtr p_cell_B = rCellPopulation.GetCellUsingLocationIndex(nodeBGlobalIndex);
 
    double ageA = p_cell_A->GetAge();
    double ageB = p_cell_B->GetAge();
 
    assert(!std::isnan(ageA));
    assert(!std::isnan(ageB));
 
    /*
     * If the cells are both newly divided, then the rest length of the spring
     * connecting them grows linearly with time, until mMeinekeSpringGrowthDuration hour after division.
     */
    if (ageA < mMeinekeSpringGrowthDuration && ageB < mMeinekeSpringGrowthDuration)
    {
        /*
         * The spring rest length increases from a predefined small parameter
         * to a normal rest length of 1.0, over a period of one hour.
         */
        std::pair<CellPtr,CellPtr> cell_pair = p_static_cast_cell_population->CreateCellPair(p_cell_A, p_cell_B);
        if (p_static_cast_cell_population->IsMarkedSpring(cell_pair))
        {
            double lambda = mMeinekeDivisionRestingSpringLength;
            rest_length = lambda + (1.0 - lambda) * ageA/mMeinekeSpringGrowthDuration;
        }
        if (ageA+SimulationTime::Instance()->GetTimeStep() >= mMeinekeSpringGrowthDuration)
        {
            // This spring is about to go out of scope
            p_static_cast_cell_population->UnmarkSpring(cell_pair);
        }
    }
 
    double a_rest_length = rest_length*0.5;
    double b_rest_length = a_rest_length;
 
    /*
     * If either of the cells has begun apoptosis, then the length of the spring
     * connecting them decreases linearly with time.
     */
    if (p_cell_A->HasApoptosisBegun())
    {
        double time_until_death_a = p_cell_A->GetTimeUntilDeath();
        a_rest_length = a_rest_length * time_until_death_a / p_cell_A->GetApoptosisTime();
    }
    if (p_cell_B->HasApoptosisBegun())
    {
        double time_until_death_b = p_cell_B->GetTimeUntilDeath();
        b_rest_length = b_rest_length * time_until_death_b / p_cell_B->GetApoptosisTime();
    }
 
    rest_length = a_rest_length + b_rest_length;
 
    // Assert that the rest length does not exceed 1
    assert(rest_length <= 1.0+1e-12);
 
    bool is_closer_than_rest_length = true;
 
    if (distance_between_nodes - rest_length > 0)
    {
        is_closer_than_rest_length = false;
    }
 
    /*
     * Although in this class the 'spring constant' is a constant parameter, in
     * subclasses it can depend on properties of each of the cells.
     */
    double multiplication_factor = 1.0;
    multiplication_factor *= VariableSpringConstantMultiplicationFactor(nodeAGlobalIndex, nodeBGlobalIndex, rCellPopulation, is_closer_than_rest_length);
 
    // Calculate the 3D force between the two points
    c_vector<double,3> force_between_nodes = multiplication_factor * this->GetMeinekeSpringStiffness() * unit_difference * (distance_between_nodes - rest_length);
 
    // Calculate an outward normal unit vector to the tangent plane of the crypt surface at the 3D point corresponding to node B
    c_vector<double,3> outward_normal_unit_vector;
 
    double dfdr = CalculateCryptSurfaceDerivativeAtPoint(node_b_location_2d);
    double theta_B = atan2(node_b_location_2d[1], node_b_location_2d[0]); // use atan2 to determine the quadrant
    double normalization_factor = sqrt(1 + dfdr*dfdr);
 
    outward_normal_unit_vector[0] = dfdr*cos(theta_B)/normalization_factor;
    outward_normal_unit_vector[1] = dfdr*sin(theta_B)/normalization_factor;
    outward_normal_unit_vector[2] = -1.0/normalization_factor;
 
    // Calculate the projection of the force onto the plane z=0
    c_vector<double,2> projected_force_between_nodes_2d;
    double force_dot_normal = inner_prod(force_between_nodes, outward_normal_unit_vector);
 
    for (unsigned i=0; i<2; i++)
    {
        projected_force_between_nodes_2d[i] = force_between_nodes[i]
                                              - force_dot_normal*outward_normal_unit_vector[i]
                                              + force_dot_normal*outward_normal_unit_vector[2];
    }
 
    return projected_force_between_nodes_2d;
}
 
void CryptProjectionForce::AddForceContribution(AbstractCellPopulation<2>& rCellPopulation)
{
    // First work out the 3D location of each cell
    UpdateNode3dLocationMap(rCellPopulation);
 
    // Throw an exception message if not using a MeshBasedCellPopulation
    if (dynamic_cast<MeshBasedCellPopulation<2>*>(&rCellPopulation) == nullptr)
    {
        EXCEPTION("CryptProjectionForce is to be used with a subclass of MeshBasedCellPopulation only");
    }
 
    MeshBasedCellPopulation<2>* p_static_cast_cell_population = static_cast<MeshBasedCellPopulation<2>*>(&rCellPopulation);
 
    for (MeshBasedCellPopulation<2>::SpringIterator spring_iterator = p_static_cast_cell_population->SpringsBegin();
         spring_iterator != p_static_cast_cell_population->SpringsEnd();
         ++spring_iterator)
    {
        unsigned nodeA_global_index = spring_iterator.GetNodeA()->GetIndex();
        unsigned nodeB_global_index = spring_iterator.GetNodeB()->GetIndex();
 
        c_vector<double, 2> force = CalculateForceBetweenNodes(nodeA_global_index, nodeB_global_index, rCellPopulation);
        c_vector<double, 2> negative_force = -1.0 * force;
        spring_iterator.GetNodeB()->AddAppliedForceContribution(negative_force);
        spring_iterator.GetNodeA()->AddAppliedForceContribution(force);
    }
 
    if (mIncludeWntChemotaxis)
    {
        assert(WntConcentration<2>::Instance()->IsWntSetUp());
 
        for (AbstractCellPopulation<2>::Iterator cell_iter = rCellPopulation.Begin();
             cell_iter != rCellPopulation.End();
             ++cell_iter)
        {
            if (cell_iter->GetCellProliferativeType()->IsType<StemCellProliferativeType>())
            {
                c_vector<double, 2> wnt_chemotactic_force = mWntChemotaxisStrength*WntConcentration<2>::Instance()->GetWntGradient(*cell_iter);
                unsigned index = rCellPopulation.GetLocationIndexUsingCell(*cell_iter);
 
                rCellPopulation.GetNode(index)->AddAppliedForceContribution(wnt_chemotactic_force);
            }
        }
    }
}
 
void CryptProjectionForce::OutputForceParameters(out_stream& rParamsFile)
{
    *rParamsFile << "\t\t\t<A>" << mA << "</A>\n";
    *rParamsFile << "\t\t\t<B>" << mB << "</B>\n";
    *rParamsFile << "\t\t\t<IncludeWntChemotaxis>" << mIncludeWntChemotaxis << "</IncludeWntChemotaxis>\n";
    *rParamsFile << "\t\t\t<WntChemotaxisStrength>" << mWntChemotaxisStrength << "</WntChemotaxisStrength>\n";
 
    // Call method on direct parent class
    GeneralisedLinearSpringForce<2>::OutputForceParameters(rParamsFile);
}
 
// Serialization for Boost >= 1.36
#include "SerializationExportWrapperForCpp.hpp"
CHASTE_CLASS_EXPORT(CryptProjectionForce)