OffLatticeMigrationRule.cpp

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#include "GeometryTools.hpp"
#include "OffLatticeMigrationRule.hpp"
#include "RandomNumberGenerator.hpp"
#include "BaseUnits.hpp"

template<unsigned DIM>
OffLatticeMigrationRule<DIM>::OffLatticeMigrationRule()
    : AbstractMigrationRule<DIM>(),
      mGlobalX(unit_vector<double>(3,0)),
      mGlobalY(unit_vector<double>(3,1)),
      mGlobalZ(unit_vector<double>(3,2)),
      mMeanAngles(std::vector<units::quantity<unit::plane_angle> >(3, 0.0*unit::radians)),
      mSdvAngles(std::vector<units::quantity<unit::plane_angle> >(3, M_PI/18.0*unit::radians)),
      mVelocity(20.0 *(1.e-6/3600.0) * unit::metre_per_second),
      mChemotacticStrength(1.0),
      mAttractionStrength(1.0),
      mProbeLength(5.0 * 1.e-6 * unit::metres),
      mCriticalMutualAttractionLength(100.0 * 1.e-6 *unit::metres)
{

}

template <unsigned DIM>
boost::shared_ptr<OffLatticeMigrationRule<DIM> > OffLatticeMigrationRule<DIM>::Create()
{
    MAKE_PTR(OffLatticeMigrationRule<DIM>, pSelf);
    return pSelf;
}

template<unsigned DIM>
OffLatticeMigrationRule<DIM>::~OffLatticeMigrationRule()
{

}

template<unsigned DIM>
void OffLatticeMigrationRule<DIM>::SetSproutingVelocity(units::quantity<unit::velocity> velocity)
{
    mVelocity = velocity;
}

template<unsigned DIM>
void OffLatticeMigrationRule<DIM>::SetChemotacticStrength(double strength)
{
    mChemotacticStrength = strength;
}

template<unsigned DIM>
void OffLatticeMigrationRule<DIM>::SetAttractionStrength(double strength)
{
    mAttractionStrength = strength;
}

template<unsigned DIM>
std::vector<DimensionalChastePoint<DIM> > OffLatticeMigrationRule<DIM>::GetDirections(const std::vector<boost::shared_ptr<VesselNode<DIM> > >& rNodes)
{
    if (this->mIsSprouting)
    {
        return GetDirectionsForSprouts(rNodes);
    }
    else
    {
        std::vector<DimensionalChastePoint<DIM> > movement_vectors;

        // We want to probe the PDE solution all at once first if needed, as this is an expensive operation if done node-by-node.
        // Every node has 5 probes in 2D and 7 in 3D.
        std::vector<units::quantity<unit::concentration> > probed_solutions;
        unsigned probes_per_node = (2*DIM)+1;
        std::vector<DimensionalChastePoint<DIM> > probe_locations(probes_per_node*rNodes.size(), DimensionalChastePoint<DIM>(0.0, 0.0, 0.0, 1.e-6*unit::metres));
        std::vector<bool> candidate_locations_inside_domain(probes_per_node*rNodes.size(), true);

        if(this->mpSolver)
        {
            for(unsigned idx=0; idx<rNodes.size(); idx++)
            {
                std::vector<DimensionalChastePoint<DIM> > local_probe_locations = GetProbeLocationsExternalPoint<DIM>(rNodes[idx]->rGetLocation(), mProbeLength);
                for(unsigned jdx=0;jdx<probes_per_node; jdx++)
                {
                    probe_locations[idx*probes_per_node + jdx] = local_probe_locations[jdx];
                }
            }
            if(probe_locations.size()>0)
            {
                probed_solutions = this->mpSolver->GetConcentrations(probe_locations);
            }

            if (this->mpBoundingDomain)
            {
                candidate_locations_inside_domain = this->mpBoundingDomain->IsPointInPart(probe_locations);
            }
        }

        for(unsigned idx=0; idx<rNodes.size(); idx++)
        {
            // Persistent random walk
            units::quantity<unit::plane_angle> angle_x =
                    RandomNumberGenerator::Instance()->NormalRandomDeviate(mMeanAngles[0]/unit::radians, mSdvAngles[0]/unit::radians)*unit::radians;
            units::quantity<unit::plane_angle> angle_y =
                    RandomNumberGenerator::Instance()->NormalRandomDeviate(mMeanAngles[1]/unit::radians, mSdvAngles[1]/unit::radians)*unit::radians;
            units::quantity<unit::plane_angle> angle_z =
                    RandomNumberGenerator::Instance()->NormalRandomDeviate(mMeanAngles[2]/unit::radians, mSdvAngles[2]/unit::radians)*unit::radians;
            DimensionalChastePoint<DIM> currentDirection = rNodes[idx]->rGetLocation()-rNodes[idx]->GetSegments()[0]->GetOppositeNode(rNodes[idx])->rGetLocation();
            c_vector<double, DIM> new_direction;
            if(DIM==3)
            {
                c_vector<double, DIM> new_direction_z = RotateAboutAxis<DIM>(currentDirection.GetUnitVector(), mGlobalZ, angle_z);
                c_vector<double, DIM> new_direction_y = RotateAboutAxis<DIM>(new_direction_z, mGlobalY, angle_y);
                new_direction = RotateAboutAxis<DIM>(new_direction_y, mGlobalX, angle_x);
                new_direction /= norm_2(new_direction);
            }
            else
            {
                new_direction = RotateAboutAxis<DIM>(currentDirection.GetUnitVector(), mGlobalZ, angle_z);
                new_direction /= norm_2(new_direction);
            }

            // Chemotaxis
            if(this->mpSolver)
            {
                // Get the gradients
                std::vector<units::quantity<unit::concentration_gradient> > gradients(probes_per_node-1, 0.0*unit::mole_per_metre_pow_4);
                if(probed_solutions.size()>=idx*probes_per_node+probes_per_node)
                {
                    for(unsigned jdx=1; jdx<probes_per_node; jdx++)
                    {
                        gradients[jdx-1] = ((probed_solutions[idx*probes_per_node+jdx] - probed_solutions[idx*probes_per_node]) / mProbeLength);
                        if(!candidate_locations_inside_domain[idx*probes_per_node+jdx])
                        {
                            gradients[jdx-1] = 0.0*unit::mole_per_metre_pow_4;
                        }
                    }
                }

                // Get the index of the max viable gradient
                units::quantity<unit::concentration_gradient> max_grad = 0.0 * unit::mole_per_metre_pow_4;
                int my_index = -1;

                for(unsigned jdx = 0; jdx<gradients.size(); jdx++)
                {
                    if(gradients[jdx]>max_grad)
                    {
                        max_grad = gradients[jdx];
                        my_index = int(jdx);
                    }
                }

                if(my_index == 0)
                {
                    new_direction += mChemotacticStrength* unit_vector<double>(DIM,0);
                }
                else if(my_index == 1)
                {
                    new_direction += mChemotacticStrength*-unit_vector<double>(DIM,0);
                }
                else if(my_index == 2)
                {
                    new_direction += mChemotacticStrength*unit_vector<double>(DIM,1);
                }
                else if(my_index == 3)
                {
                    new_direction += mChemotacticStrength*-unit_vector<double>(DIM,1);
                }
                else if(my_index == 4)
                {
                    new_direction += mChemotacticStrength*unit_vector<double>(DIM,2);
                }
                else if(my_index == 5)
                {
                    new_direction += mChemotacticStrength*-unit_vector<double>(DIM,2);
                }
            }
            new_direction /= norm_2(new_direction);

            // Mutual Attraction
            std::vector<boost::shared_ptr<VesselNode<DIM> > > nodes = this->mpVesselNetwork->GetNodes();
            units::quantity<unit::length> min_distance = 1.e12*unit::metres;
            c_vector<double, DIM> min_direction = zero_vector<double>(DIM);
            units::quantity<unit::length> reference_length = currentDirection.GetReferenceLengthScale();
            for(unsigned jdx=0; jdx<nodes.size(); jdx++)
            {
                if(IsPointInCone<DIM>(nodes[jdx]->rGetLocation(), rNodes[idx]->rGetLocation(), rNodes[idx]->rGetLocation() +
                                      DimensionalChastePoint<DIM>(currentDirection.GetLocation(reference_length) * double(mCriticalMutualAttractionLength/reference_length), reference_length), M_PI/3.0))
                {
                    units::quantity<unit::length> distance = rNodes[idx]->rGetLocation().GetDistance(nodes[jdx]->rGetLocation());
                    if(distance < min_distance)
                    {
                        min_distance = distance;
                        DimensionalChastePoint<DIM> dim_min_direction = nodes[jdx]->rGetLocation() - rNodes[idx]->rGetLocation();
                        min_direction = dim_min_direction.GetUnitVector();
                    }
                }
            }

            double strength = 0.0;
            if(min_distance < mCriticalMutualAttractionLength)
            {
                strength = mAttractionStrength *  (1.0 - (min_distance * min_distance) / (mCriticalMutualAttractionLength * mCriticalMutualAttractionLength));
            }
            new_direction += strength * min_direction;
            new_direction /= norm_2(new_direction);

            // Get the movement increment
            units::quantity<unit::time> time_increment = SimulationTime::Instance()->GetTimeStep()*BaseUnits::Instance()->GetReferenceTimeScale();
            units::quantity<unit::length> increment_length = time_increment* mVelocity;
            movement_vectors.push_back(OffsetAlongVector<DIM>(new_direction, increment_length, reference_length));
        }
        return movement_vectors;
    }
}

template<unsigned DIM>
std::vector<DimensionalChastePoint<DIM> > OffLatticeMigrationRule<DIM>::GetDirectionsForSprouts(const std::vector<boost::shared_ptr<VesselNode<DIM> > >& rNodes)
{
    std::vector<DimensionalChastePoint<DIM> > movement_vectors;
    units::quantity<unit::length> reference_length = BaseUnits::Instance()->GetReferenceLengthScale();

    // Collect the probe locations for each node
    std::vector<units::quantity<unit::concentration> > probed_solutions;
    unsigned probes_per_node = 3;
    if(DIM==3)
    {
        probes_per_node = 5;
    }
    std::vector<DimensionalChastePoint<DIM> > probe_locations(probes_per_node*rNodes.size(), DimensionalChastePoint<DIM>(0.0, 0.0, 0.0, reference_length));
    std::vector<bool> candidate_locations_inside_domain(probes_per_node*rNodes.size(), true);

    // Get a normal to the segments, will depend on whether they are parallel
    for(unsigned idx = 0; idx < rNodes.size(); idx++)
    {
        c_vector<double, DIM> sprout_direction;
        c_vector<double, DIM> cross_product;
        double sum = 0.0;

        if(DIM==3)
        {
            cross_product = VectorProduct(rNodes[idx]->GetSegments()[0]->GetUnitTangent(),
                                                                rNodes[idx]->GetSegments()[1]->GetUnitTangent());
            for(unsigned jdx=0; jdx<DIM; jdx++)
            {
                sum += abs(cross_product[jdx]);
            }
        }
        else
        {
            c_vector<double, DIM> tangent1 = rNodes[idx]->GetSegments()[0]->GetUnitTangent();
            c_vector<double, DIM> tangent2 = rNodes[idx]->GetSegments()[1]->GetUnitTangent();
            for(unsigned jdx=0; jdx<DIM; jdx++)
            {
                sum += abs(tangent1[jdx]-tangent2[jdx]);
            }
        }

        if (sum<=1.e-6)
        {
            // more or less parallel segments, chose any normal to the first tangent
            c_vector<double, DIM> normal;
            c_vector<double, DIM> tangent = rNodes[idx]->GetSegments()[0]->GetUnitTangent();
            if(DIM==2 or tangent[2]==0.0)
            {
                if(tangent[1] == 0.0)
                {
                    normal[0] = 0.0;
                    normal[1] = 1.0;
                }
                else
                {
                    normal[0] = 1.0;
                    normal[1] = -tangent[0] /tangent[1];
                }
            }
            else
            {
                if(std::abs(tangent[0]) + std::abs(tangent[1]) == 0.0)
                {
                    normal[0] = 1.0;
                    normal[1] = 1.0;
                }
                else
                {
                    normal[0] = 1.0;
                    normal[1] = 1.0;
                    normal[2] = -(tangent[0] + tangent[1])/tangent[2];
                }
            }
            if(RandomNumberGenerator::Instance()->ranf()>=0.5)
            {
                sprout_direction = normal/norm_2(normal);
            }
            else
            {
                sprout_direction = -normal/norm_2(normal);
            }
        }
        else
        {
            if(DIM==3)
            {
                // otherwise the direction is out of the plane of the segment tangents
                if(RandomNumberGenerator::Instance()->ranf()>=0.5)
                {
                    sprout_direction = cross_product/norm_2(cross_product);
                }
                else
                {
                    sprout_direction = -cross_product/norm_2(cross_product);
                }
            }
            else
            {
                c_vector<double, DIM> tangent1 = rNodes[idx]->GetSegments()[0]->GetUnitTangent();
                c_vector<double, DIM> tangent2 = rNodes[idx]->GetSegments()[1]->GetUnitTangent();
                c_vector<double, DIM> av_tangent = (tangent1 + tangent2)/2.0;
                av_tangent/=norm_2(av_tangent);

                c_vector<double, DIM> normal;
                if(av_tangent[1] == 0.0)
                {
                    normal[0] = 0.0;
                    normal[1] = 1.0;
                }
                else
                {
                    normal[0] = 1.0;
                    normal[1] = -av_tangent[0] /av_tangent[1];
                }

                if(RandomNumberGenerator::Instance()->ranf()>=0.5)
                {
                    sprout_direction = normal/norm_2(normal);
                }
                else
                {
                    sprout_direction = -normal/norm_2(normal);
                }
            }
        }

        units::quantity<unit::plane_angle> angle = RandomNumberGenerator::Instance()->NormalRandomDeviate(mMeanAngles[0]/unit::radians,
                                                                                                          mSdvAngles[0]/unit::radians)*unit::radians;
        std::vector<DimensionalChastePoint<DIM> > local_probes = GetProbeLocationsInternalPoint<DIM>(DimensionalChastePoint<DIM>(sprout_direction, reference_length),
                                                                                                rNodes[idx]->rGetLocation(),
                                                                                                DimensionalChastePoint<DIM>(rNodes[idx]->GetSegments()[0]->GetUnitTangent(), reference_length),
                                                                                                mProbeLength,
                                                                                                angle);
        for(unsigned jdx=0;jdx<probes_per_node; jdx++)
        {
            probe_locations[idx*probes_per_node + jdx] = local_probes[jdx];
        }
    }

    if(this->mpSolver)
    {
        if(probe_locations.size()>0)
        {
            probed_solutions = this->mpSolver->GetConcentrations(probe_locations);
        }

        if (this->mpBoundingDomain)
        {
            candidate_locations_inside_domain = this->mpBoundingDomain->IsPointInPart(probe_locations);
        }
    }

    // Decide on the sprout directions
    for(unsigned idx=0; idx<rNodes.size(); idx++)
    {
        DimensionalChastePoint<DIM> new_direction(0.0, 0.0, 0.0, reference_length);

        // Solution dependent contribution
        if(this->mpSolver)
        {
            // Get the gradients
            std::vector<units::quantity<unit::concentration_gradient> > gradients(probes_per_node-1, 0.0*unit::mole_per_metre_pow_4);
            if(probed_solutions.size()>=idx*probes_per_node+probes_per_node)
            {
                for(unsigned jdx=1; jdx<probes_per_node; jdx++)
                {
                    gradients[jdx-1] = ((probed_solutions[idx*probes_per_node+jdx] - probed_solutions[idx*probes_per_node]) / mProbeLength);
                    if(!candidate_locations_inside_domain[idx*probes_per_node+jdx])
                    {
                        gradients[jdx-1] = 0.0*unit::mole_per_metre_pow_4;
                    }
                }
            }

            // Get the index of the max viable gradient
            units::quantity<unit::concentration_gradient> max_grad = 0.0 * unit::mole_per_metre_pow_4;
            int my_index = -1;
            for(unsigned jdx = 0; jdx<gradients.size(); jdx++)
            {
                if(gradients[jdx]>max_grad)
                {
                    max_grad = gradients[jdx];
                    my_index = int(jdx);
                }
            }
            if(my_index == 0)
            {
                new_direction = probe_locations[idx*probes_per_node+1]-rNodes[idx]->rGetLocation();
            }
            else if(my_index == 1)
            {
                new_direction = probe_locations[idx*probes_per_node+2]-rNodes[idx]->rGetLocation();
            }
            else if(my_index == 2)
            {
                new_direction = probe_locations[idx*probes_per_node+3]-rNodes[idx]->rGetLocation();
            }
            else if(my_index == 3)
            {
                new_direction = probe_locations[idx*probes_per_node+4]-rNodes[idx]->rGetLocation();
            }
        }

        units::quantity<unit::time> time_increment = SimulationTime::Instance()->GetTimeStep()*BaseUnits::Instance()->GetReferenceTimeScale();
        units::quantity<unit::length> increment_length = time_increment* mVelocity;
        movement_vectors.push_back(OffsetAlongVector<DIM>(new_direction, increment_length));
    }

    return movement_vectors;
}

// Explicit instantiation
template class OffLatticeMigrationRule<2> ;
template class OffLatticeMigrationRule<3> ;