GeneralisedLinearSpringForce.cpp

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*/

#include "GeneralisedLinearSpringForce.hpp"

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
GeneralisedLinearSpringForce<ELEMENT_DIM,SPACE_DIM>::GeneralisedLinearSpringForce()
   : AbstractTwoBodyInteractionForce<ELEMENT_DIM,SPACE_DIM>(),
     mMeinekeSpringStiffness(15.0),        // denoted by mu in Meineke et al, 2001 (doi:10.1046/j.0960-7722.2001.00216.x)
     mMeinekeDivisionRestingSpringLength(0.5),
     mMeinekeSpringGrowthDuration(1.0)
{
    if (SPACE_DIM == 1)
    {
        mMeinekeSpringStiffness = 30.0;
    }
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
double GeneralisedLinearSpringForce<ELEMENT_DIM,SPACE_DIM>::VariableSpringConstantMultiplicationFactor(unsigned nodeAGlobalIndex,
                                                                                     unsigned nodeBGlobalIndex,
                                                                                     AbstractCellPopulation<ELEMENT_DIM,SPACE_DIM>& rCellPopulation,
                                                                                     bool isCloserThanRestLength)
{
    return 1.0;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
GeneralisedLinearSpringForce<ELEMENT_DIM,SPACE_DIM>::~GeneralisedLinearSpringForce()
{
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
c_vector<double, SPACE_DIM> GeneralisedLinearSpringForce<ELEMENT_DIM,SPACE_DIM>::CalculateForceBetweenNodes(unsigned nodeAGlobalIndex,
                                                                                    unsigned nodeBGlobalIndex,
                                                                                    AbstractCellPopulation<ELEMENT_DIM,SPACE_DIM>& rCellPopulation)
{
    // We should only ever calculate the force between two distinct nodes
    assert(nodeAGlobalIndex != nodeBGlobalIndex);

    // Get the node locations
    c_vector<double, SPACE_DIM> node_a_location = rCellPopulation.GetNode(nodeAGlobalIndex)->rGetLocation();
    c_vector<double, SPACE_DIM> node_b_location = rCellPopulation.GetNode(nodeBGlobalIndex)->rGetLocation();

    // Get the node radii for a NodeBasedCellPopulation
    double node_a_radius=0.0;
    double node_b_radius=0.0;

    if (dynamic_cast<NodeBasedCellPopulation<SPACE_DIM>*>(&rCellPopulation))
    {
        node_a_radius = dynamic_cast<NodeBasedCellPopulation<SPACE_DIM>*>(&rCellPopulation)->rGetMesh().GetCellRadius(nodeAGlobalIndex);
        node_b_radius = dynamic_cast<NodeBasedCellPopulation<SPACE_DIM>*>(&rCellPopulation)->rGetMesh().GetCellRadius(nodeBGlobalIndex);
    }

    // Get the unit vector parallel to the line joining the two nodes
    c_vector<double, SPACE_DIM> unit_difference;
    if (dynamic_cast<MeshBasedCellPopulation<ELEMENT_DIM,SPACE_DIM>*>(&rCellPopulation))
    {
        /*
         * We use the mesh method GetVectorFromAtoB() to compute the direction of the
         * unit vector along the line joining the two nodes, rather than simply subtract
         * their positions, because this method can be overloaded (e.g. to enforce a
         * periodic boundary in Cylindrical2dMesh).
         */
        unit_difference = (static_cast<MeshBasedCellPopulation<ELEMENT_DIM,SPACE_DIM>*>(&rCellPopulation))->rGetMesh().GetVectorFromAtoB(node_a_location, node_b_location);
    }
    else
    {
        unit_difference = node_b_location - node_a_location;
    }

    // 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 mMechanicsCutOffLength in AbstractTwoBodyInteractionForce.
     */
    if (this->mUseCutOffLength)
    {
        if (distance_between_nodes >= this->GetCutOffLength())
        {
            return zero_vector<double>(SPACE_DIM); // c_vector<double,SPACE_DIM>() is not guaranteed to be fresh memory
        }
    }

    /*
     * Calculate the rest length of the spring connecting the two nodes with a default
     * value of 1.0.
     */
    double rest_length_final = 1.0;

    if (dynamic_cast<MeshBasedCellPopulation<ELEMENT_DIM,SPACE_DIM>*>(&rCellPopulation))
    {
        rest_length_final = static_cast<MeshBasedCellPopulation<ELEMENT_DIM,SPACE_DIM>*>(&rCellPopulation)->GetRestLength(nodeAGlobalIndex, nodeBGlobalIndex);
    }
    else if (dynamic_cast<NodeBasedCellPopulation<SPACE_DIM>*>(&rCellPopulation))
    {
        assert(node_a_radius > 0 && node_b_radius > 0);
        rest_length_final = node_a_radius+node_b_radius;
    }

    double rest_length = rest_length_final;

    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 1 hour after division.
     */
    if (ageA < mMeinekeSpringGrowthDuration && ageB < mMeinekeSpringGrowthDuration)
    {
        AbstractCentreBasedCellPopulation<ELEMENT_DIM,SPACE_DIM>* p_static_cast_cell_population = static_cast<AbstractCentreBasedCellPopulation<ELEMENT_DIM,SPACE_DIM>*>(&rCellPopulation);

        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))
        {
            // Spring rest length increases from a small value to the normal rest length over 1 hour
            double lambda = mMeinekeDivisionRestingSpringLength;
            rest_length = lambda + (rest_length_final - 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);
        }
    }

    /*
     * For apoptosis, progressively reduce the radius of the cell
     */
    double a_rest_length = rest_length*0.5;
    double b_rest_length = a_rest_length;

    if (dynamic_cast<NodeBasedCellPopulation<SPACE_DIM>*>(&rCellPopulation))
    {
        assert(node_a_radius > 0 && node_b_radius > 0);
        a_rest_length = (node_a_radius/(node_a_radius+node_b_radius))*rest_length;
        b_rest_length = (node_b_radius/(node_a_radius+node_b_radius))*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(rest_length <= 1.0+1e-12); ///\todo #1884 Magic number: would "<= 1.0" do?


    // Although in this class the 'spring constant' is a constant parameter, in
    // subclasses it can depend on properties of each of the cells
    double overlap = distance_between_nodes - rest_length;
    bool is_closer_than_rest_length = (overlap <= 0);
    double multiplication_factor = VariableSpringConstantMultiplicationFactor(nodeAGlobalIndex, nodeBGlobalIndex, rCellPopulation, is_closer_than_rest_length);
    double spring_stiffness = mMeinekeSpringStiffness;

    if (dynamic_cast<MeshBasedCellPopulation<ELEMENT_DIM,SPACE_DIM>*>(&rCellPopulation))
    {
        return multiplication_factor * spring_stiffness * unit_difference * overlap;
    }
    else
    {
        // A reasonably stable simple force law
        if (is_closer_than_rest_length) //overlap is negative
        {
            //log(x+1) is undefined for x<=-1
            assert(overlap > -rest_length_final);
            c_vector<double, SPACE_DIM> temp = spring_stiffness * unit_difference * rest_length_final* log(1.0 + overlap/rest_length_final);
            return temp;
        }
        else
        {
            double alpha = 5.0;
            c_vector<double, SPACE_DIM> temp = spring_stiffness * unit_difference * overlap * exp(-alpha * overlap/rest_length_final);
            return temp;
        }
    }
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
double GeneralisedLinearSpringForce<ELEMENT_DIM,SPACE_DIM>::GetMeinekeSpringStiffness()
{
    return mMeinekeSpringStiffness;
}
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
double GeneralisedLinearSpringForce<ELEMENT_DIM,SPACE_DIM>::GetMeinekeDivisionRestingSpringLength()
{
    return mMeinekeDivisionRestingSpringLength;
}
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
double GeneralisedLinearSpringForce<ELEMENT_DIM,SPACE_DIM>::GetMeinekeSpringGrowthDuration()
{
    return mMeinekeSpringGrowthDuration;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void GeneralisedLinearSpringForce<ELEMENT_DIM,SPACE_DIM>::SetMeinekeSpringStiffness(double springStiffness)
{
    assert(springStiffness > 0.0);
    mMeinekeSpringStiffness = springStiffness;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void GeneralisedLinearSpringForce<ELEMENT_DIM,SPACE_DIM>::SetMeinekeDivisionRestingSpringLength(double divisionRestingSpringLength)
{
    assert(divisionRestingSpringLength <= 1.0);
    assert(divisionRestingSpringLength >= 0.0);

    mMeinekeDivisionRestingSpringLength = divisionRestingSpringLength;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void GeneralisedLinearSpringForce<ELEMENT_DIM,SPACE_DIM>::SetMeinekeSpringGrowthDuration(double springGrowthDuration)
{
    assert(springGrowthDuration >= 0.0);

    mMeinekeSpringGrowthDuration = springGrowthDuration;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void GeneralisedLinearSpringForce<ELEMENT_DIM,SPACE_DIM>::OutputForceParameters(out_stream& rParamsFile)
{
    *rParamsFile << "\t\t\t<MeinekeSpringStiffness>" << mMeinekeSpringStiffness << "</MeinekeSpringStiffness>\n";
    *rParamsFile << "\t\t\t<MeinekeDivisionRestingSpringLength>" << mMeinekeDivisionRestingSpringLength << "</MeinekeDivisionRestingSpringLength>\n";
    *rParamsFile << "\t\t\t<MeinekeSpringGrowthDuration>" << mMeinekeSpringGrowthDuration << "</MeinekeSpringGrowthDuration>\n";

    // Call method on direct parent class
    AbstractTwoBodyInteractionForce<ELEMENT_DIM,SPACE_DIM>::OutputForceParameters(rParamsFile);
}

// Explicit instantiation

template class GeneralisedLinearSpringForce<1,1>;
template class GeneralisedLinearSpringForce<1,2>;
template class GeneralisedLinearSpringForce<2,2>;
template class GeneralisedLinearSpringForce<1,3>;
template class GeneralisedLinearSpringForce<2,3>;
template class GeneralisedLinearSpringForce<3,3>;

// Serialization for Boost >= 1.36
#include "SerializationExportWrapperForCpp.hpp"
EXPORT_TEMPLATE_CLASS_ALL_DIMS(GeneralisedLinearSpringForce)